4.7
Converting from Decimals
to Fractions
4.7
OBJECTIVES
1. Convert a decimal to a common fraction
Using what we have learned about place values, you can easily write decimals as common
fractions. The following rule is used.
Step by Step: To Convert a Terminating Decimal Less Than
1 to a Common Fraction
Step 1 Write the digits of the decimal without the decimal point. This will be
the numerator of the common fraction.
Step 2 The denominator of the fraction is a 1 followed by as many zeros as
there are places in the decimal.
Example 1
Converting a Decimal to a Common Fraction
One place
One zero
0.09 Two places
9
100
Two zeros
0.257 7
10
0.7 Three places
257
1000
Three zeros
CHECK YOURSELF 1
Write as common fractions.
(a) 0.3
(b) 0.311
When a decimal is converted to a common fraction, the common fraction that results
should be written in lowest terms.
© 2001 McGraw-Hill Companies
Example 2
Converting a Decimal to a Common Fraction
Convert 0.395 to a fraction and write the result in lowest terms.
NOTE Divide the numerator
and denominator by 5.
0.395 395
79
1000
200
CHECK YOURSELF 2
Write 0.275 as a common fraction.
379
380
CHAPTER 4
DECIMALS
If the decimal has a whole-number portion, write the digits to the right of the decimal
point as a proper fraction and then form a mixed number for your result.
Example 3
also be written as common
fractions, although the process
is more complicated. We will
limit ourselves to the
conversion of terminating
decimals in this textbook.
Converting a Decimal to a Mixed Number
Write 12.277 as a mixed number.
0.277 277
277
, so 12.277 12
1000
1000
CHECK YOURSELF 3
Write 32.433 as a mixed number.
Comparing the sizes of common fractions and decimals requires finding the decimal
equivalent of the common fraction and then comparing the resulting decimals.
Example 4
Comparing the Sizes of Common Fractions and Decimals
Which is larger,
3
or 0.38?
8
3
Write the decimal equivalent of . That decimal is 0.375. Now comparing 0.375 and
8
0.38, we see that 0.38 is the larger of the numbers:
0.38 3
8
CHECK YOURSELF 4
Which is larger,
3
or 0.8?
4
CHECK YOURSELF ANSWERS
1. (a)
3
311
; (b)
10
1000
2. 0.275 11
40
3. 32
433
1000
4. 0.8 3
4
© 2001 McGraw-Hill Companies
NOTE Repeating decimals can
Name
4.7
Exercises
Section
Date
Write each of the following as a common fraction or mixed number. Write your answer in
lowest terms.
ANSWERS
1. 0.9
2. 0.3
1.
2.
3.
4.
3. 0.8
4. 0.6
5. 0.37
6. 0.97
5.
6.
7. 0.587
8. 0.3793
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
9. 0.48
10. 0.75
11. 0.58
12. 0.65
13. 0.425
14. 0.116
15. 0.375
16. 0.225
17. 0.136
18. 0.575
19.
20.
19. 0.059
20. 0.067
21.
22.
21. 0.0625
22. 0.0425
23.
24.
23. 6.3
24. 5.7
25.
26.
25. 2.17
26. 3.31
27.
© 2001 McGraw-Hill Companies
27. 5.28
28. 15.35
Complete each of the following statements, using the symbol or .
7
29. _____ 0.87
8
5
30.
_____ 0.313
16
9
_____ 0.4
31.
25
11
_____ 0.638
32.
17
28.
29.
30.
31.
32.
381
ANSWERS
33. The following table gives the winning percentage for the teams in the American
33.
League West. What fraction of their games has each team won?
34.
Team
Winning Percentage
Texas
Oakland
Seattle
Anaheim
0.595
0.552
0.494
0.415
34. The following table gives the winning percentages of the top five coaches in NFL
history. What fraction of his games has each coach won?
Coach
Percentage
Don Shula
George Halas
Tom Landry
Curly Lambeau
Chuck Knoll
0.676
0.672
0.606
0.624
0.566
9
10
3
15.
8
1.
27. 5
382
4
5
3.
17.
7
25
5.
17
125
29. 37
100
19.
7.
59
1000
31. 587
1000
9.
12
25
11.
29
50
1
3
23. 6
16
10
119 69 247 83
,
,
,
33.
200 125 500 200
21.
13.
25. 2
17
100
17
40
© 2001 McGraw-Hill Companies
Answers
Using Your Calculator to
Convert Between Decimals
and Fractions
A calculator is very useful in converting common fractions to decimals. Just divide the
numerator by the denominator, and the decimal equivalent will be in the display.
Example 1
Converting Fractions to Decimals
Find the decimal equivalent of
7
.
16
7 16 Display 0.4375
0.4375 is the decimal equivalent of
7
.
16
CHECK YOURSELF 1
Find the decimal equivalent of
5
.
16
Often, you will want to round the result in the display.
Example 2
Converting Fractions to Decimals
NOTE Some calculators show
Find the decimal equivalent of
the 0 to the left of the decimal
point and seven digits to the
right. Others omit the 0 and
show eight digits to the right.
Check yours with this example.
5 24 Display 0.2083333
5
0.21
24
© 2001 McGraw-Hill Companies
5
to the nearest hundredth.
24
(nearest hundredth)
CHECK YOURSELF 2
Find the decimal equivalent of
7
to the nearest hundredth.
29
To find the decimal equivalent of a mixed number, use the following sequence.
383
384
CHAPTER 4
DECIMALS
Example 3
NOTE There are several ways
to do this, depending on the
calculator you are using. For
example,
Converting Mixed Numbers to Decimals
5
Change 7 to a decimal.
8
7 5 8 5 8 7 Display 7.625
CHECK YOURSELF 3
3
Find the decimal equivalent of 3 .
8
Depending on the calculator you are using, the result may be rounded at its last displayed
digit.
Example 4
Converting Fractions to Decimals
5
For :
9
5 9 Display 0.555555555 or 0.5555555556
Rounded display
CHECK YOURSELF 4
Find the decimal equivalent of
7
.
11
CHECK YOURSELF ANSWERS
1. 0.3125
2. 0.24
3. 3.375
4. 0.63636363 or 0.63636364
© 2001 McGraw-Hill Companies
will work on most scientific
calculators. Try it on yours.
Name
Calculator Exercises
Section
Date
Find the decimal equivalents.
1.
7
8
2.
11
16
ANSWERS
1.
2.
3.
9
16
4.
7
hundredth
24
3.
4.
5.
5.
5
thousandth
32
6.
11
thousandth
75
6.
7.
8.
7.
3
use bar notation
11
8.
7
use bar notation
11
9.
10.
11.
16
9.
use bar notation
33
4
10. 3
5
12.
13.
14.
11. 3
7
8
12. 8
3
16
15.
16.
17.
© 2001 McGraw-Hill Companies
Convert each decimal to a fraction.
13. 0.3
14. 0.55
15. 0.305
16. 0.1
17. 0.875
18. 0.125
18.
385
Answers
1. 0.875
3. 0.5625
61
15.
200
5. 0.156
7. 0.27
9. 0.48
11. 3.875
7
17.
8
© 2001 McGraw-Hill Companies
3
13.
10
386